(6) His irremediable racism, even by 1910s standards
What? Can you give examples? He invited Booker T. Washington to the White House (a highly unpopular more at the time). When criticized about it he said: "I had no thought whatever of anything save of having a chance of showing some little respect to a man whom I cordially esteem as a good citizen and a good American. The outburst of feeling is to me literally inexplicable"
Other quotes:
"I should hang my head in shame if I were capable of discriminating against a man because he and I have different shades of skin"
"The wise and honorable Christian thing to do is treat each black man and each white man on his merits as a man"
"At Santiago [I served] beside black troops. A man who is good enough to shed blood for his country is good enough to be given a square deal afterward"
What Roosevelt said, and what he did, are two different things: His intervention in the Brownsville Riot of 1906 being the best example of his racism, in addition to his lusty support for the extralegal lynchings taking place in the South. Another is the Gentleman's Agreement with China--yes, most (virtually all) Americans despised the Chinese; never before, though, had that prejudice actually been made a law.
Uh...ever heard of the Chinese Exclusion Act?
Now, Teddy Roosevelt is hardly my favourite choice to win this thing. But compared with some others, he made relatively few enemies right and left (same as Harry Truman, btw.) These two making up the final came as no surprise.